Representations of Coxeter groups and homology of Coxeter graphs
Hongsheng Hu

TL;DR
This paper classifies a new class of complex representations of Coxeter groups using graph homology, generalizing geometric representations and analyzing their structure through Kazhdan-Lusztig theory.
Contribution
It introduces a novel classification of Coxeter group representations via graph homology and describes the associated cell representations and their simple quotients.
Findings
Classified a new class of Coxeter group representations
Connected these representations to second-highest 2-sided cells
Identified simple quotients for specific Coxeter systems
Abstract
We classify a class of complex representations of an arbitrary Coxeter group via characters of the integral homology of certain graphs. Such representations can be viewed as a generalization of the geometric representation and correspond to the second-highest 2-sided cell in the sense of Kazhdan-Lusztig. We also give a description of the cell representation provided by this 2-sided cell, and find out all its simple quotients for simply laced Coxeter system with no more than one circuit in the Coxeter graph.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Algebra and Geometry
